Q. 1 F5.0( 2 Votes )

Without actually performing the long division, state whether the following rational numbers have terminating or non-terminating repeating (recurring) decimal expansion.


Answer :

Given rational number is


is terminating if


a) p and q are co-prime &


b) q is of the form of 2n 5m where n and m are non-negative integers.


Firstly, we check co-prime


7 = 7 × 1


80 = 2 × 2 × 2 × 2 × 5


7 and 80 have no common factors


Therefore, 7 and 80 are co-prime.


Now, we have to check that q is in the form of 2n5m


80 = 24 × 5


So, denominator is of the form 2n5m where n = 4 and m = 1


Thus, is a terminating decimal.


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